hypotesetesting

Hypotesetesting is a formal statistical method used to assess evidence about a population parameter by comparing observed data to what would be expected under a designated null hypothesis. The process centers on two competing statements: the null hypothesis (H0) and the alternative hypothesis (H1). The null usually represents no effect or no difference, while the alternative expresses the effect or difference of interest.

The typical workflow involves formulating H0 and H1, selecting a statistical test and a significance level (alpha), calculating a test statistic from the sample, and determining a p-value or a critical value. If the p-value is at most alpha, or the statistic falls in the rejection region, H0 is rejected; otherwise, it is not rejected. A small p-value indicates that the observed data would be unlikely if H0 were true. However, failure to reject H0 does not prove it true.

Key concepts include Type I error (rejecting a true H0) and Type II error (failing to reject a false H0), together with the study’s power (the probability of correctly rejecting a false H0). Common tests include t-tests for means, z-tests, chi-square tests for proportions or categorical associations, and ANOVA for comparing multiple means; nonparametric tests offer alternatives when assumptions are violated. Analyses may be one-tailed or two-tailed, depending on the research question.

Assumptions such as random sampling, independence, and distributional conditions influence test choice and interpretation. Reporting should include the test statistic, degrees of freedom when relevant, p-value, alpha, and an effect size; a confidence interval may accompany the results to convey precision.